Vortex formation of spherical self-propelled particles around a circular obstacle

A vortex is a common ratchet phenomenon in active systems. The spatial symmetry is usually broken by introducing asymmetric shapes or spontaneously by collective motion in the presence of hydrodynamic interactions or other alignment effects. Unexpectedly, we observe, by simulations, the formation of a vortex in the simplest model of a circular obstacle immersed in a bath of spherical self-propelled particles. No symmetry-breaking factors mentioned above are included in this model. The vortex forms only when the particle activity is high, i.e. large persistence. The obstacle size is also a key factor and the vortex only forms in a limited range of obstacle sizes. The sustainment of the vortex originates from the bias of the rotating particle cluster around the obstacle in accepting the incoming particles based on their propelling directions. Our results provide new understanding of and insights into the spontaneous symmetry-breaking and ratchet phenomena in active matter.